Linearizability of homogeneous quartic polynomial systems with 1:−2 resonance

In this paper, we consider the linearizability problem of complex planar polynomial systems of the form ẋ=x+P4, ẏ=−2y−Q4, where P4P4 and Q4Q4 are homogeneous quartic polynomials. We obtain the necessary and sufficient conditions for linearizing the systems.